Unit name | Generalised Linear Models |
---|---|
Unit code | MATH35200 |
Credit points | 10 |
Level of study | H/6 |
Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |
Unit director | Dr. Liverani |
Open unit status | Not open |
Pre-requisites | |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
We study methods for the analysis of data in which one variable, the response, is influenced systematically by one or more explanatory variables, which could be qualitative or quantitative in nature, in addition to the presence of random variation. In contrast to well-known and traditional methods involving linear models and normal variation (as studied in earlier units), here we depart from linearity and normality, and need the principle of maximum likelihood to fir our models, instead of relying on least squares. The topics discussed will be: Generalised linear models: extensions of the ideas of linear modelling to deal with situations where the response variable takes integer or categorical values. These methods are particularly important in biomedical applications. Survival analysis: an introduction to regression models for lifetime data, used in clinical trials and industrial testing.
Aims
To study both theoretical and practical aspects of statistical modeling, to develop the expertise in selecting and evaluating the model and interpreting the results.
Syllabus
Overview of data analysis, motivating examples. Review of linear models. (1 lecture)
Generalized linear models (GLMs). Exponential family model, sufficiency issues. Link function, canonical link. (5 lectures)
Inference for generalized linear models, based on asymptotic theory: confidence intervals, hypothesis testing, goodness of fit. Results interpretation. Diagnostics. (4 lectures)
Binary responses, logistic regression, residuals and diagnostics. (2 lectures)
Introduction to survival analysis. Distribution theory: standard parametric models. Proportional odds model and connection to binomial GLM's. Inference assuming a parametric form for the baseline hazard. (4 lectures)
Note: the number of lectures for each topic is approximate.
Relation to Other Units
This unit builds on the basic ideas of linear models introduced in Probability and Statistics 1 (MATH 11340), and Linear Models (MATH 35110), and extends them to deal with more general specifications.
By the end of the unit, the student should have a good working understanding of:
Lectures (including both theory and examples) and practice problems.
The assessment mark for Generalized Linear Models is calculated from a 1 ½-hour written examination in May/June consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) are allowed. Statistical tables will be provided.
The range of topics covered in the unit is rather broad. Students might find the following textbooks useful
Other useful references include: